This is a scam where there is actually a ruling against the Bevis family. Read the full story in the Mirror here: The telephone preference opt-out scam.
In short, this scam is similar to their EU Health Card and Fishing Rod Licence Application cons. They find a free service, create an official-looking website (only there is nothing remotely official about it) with a confusingly similar name, often using an official image or logo without permission, and then offer the same service but with an additional fee for ‘checking’ or ‘submitting’.
However, their Telephone Preference Register service was held to be confusingly similar to the official Telephone Preference Service and ruled misleading by the Advertising Standards Authority, so they had to end it.
According to standard modus operandi their website listed a post box address in London which could in turn be traced back to Peter Bevis in Alderney, see link above.